10.5 A MODELING INVESTIGATION OF NEAR-CLOUD TURBULENCE

Todd P. Lane�, Robert Sharman and Terry L. Clark

National Center for Atmospheric Research, USA

1. Introduction

Atmospheric turbulence poses a significant risk to the avi-ation community. Such turbulence has a variety of wellknown sources, which include thunderstorms, mountainranges, and jet streams. However, the generation of tur-bulence by these sources is not particularly well under-stood. The current study seeks to investigate possiblemechanisms which cause turbulence in the clear-air sur-rounding developing thunderstorms. This study is moti-vated by a specific turbulence encounter by a commercialjet.

On 10 July 1997 a commercial passenger aircraftencountered severe turbulence near Dickinson, ND, en-route from Seattle to New York. The aircraft was nego-tiating a number of scattered thunderstorms, yet passeddirectly over a developing deep convective cloud. Whilepassing over this cloud, the aircraft suffered accelerationsof approximately two g’s, in a period of about 10 sec-onds. Subsequently, twenty passengers and two flightattendants suffered minor injuries.

The aircraft was flying at 37000 feet, which on thatday, corresponds to about 11 km above ground level(AGL): very close to the height of the tropopause. Theencountered convective cell formed between two moremature thunderstorms that were about 100 km apart. Theaircraft experienced turbulence while out of cloud and di-rectly above this center convective cell, as it overshot intothe relatively undisturbed air at the tropopause.

In an attempt to understand possible processescausing the turbulence encounter, two and three-dimensional cloud-resolving model calculations, are pre-sented. These calculations explicitly resolve both theconvection and the turbulence-causing instabilities in thevicinity of the cloud.The cloud-resolving model used inthis study was developed by Clark (1977) and Clark andFarley (1984). This model uses the anelastic approxi-mation, and has explicit treatments of cloud processesvia a combination of a Kessler (1969) warm rain parame-terization and a Koenig-Murray (1976) ice parameteriza-tion. The model also features a first-order Smagorinsky(1963)-Lilly (1962) subgrid-scale closure.

The two-dimensional model results are presented inSection 2, the results from the three-dimensional modelcalculations are presented in Section 3, and some con-clusions are presented in Section 4.

�Corresponding author address: Todd Lane, NCAR, PO BOX

3000, Boulder CO, 80307-3000 USA. E-mail: lane@ucar.edu

2. Two-dimensional simulations

The two-dimensional model domain is 200 km wide and36 km high, with a grid spacing of 50 meters in both thehorizontal and vertical directions. The uppermost 15 kmof the model domain features a Rayleigh-friction absorberto absorb vertically propagating waves with minimal re-flection. The model is initialized with wind and thermody-namic data derived from the 0Z 11 July 1997 soundingtaken at Bismarck, ND. This sounding was taken approx-imately two hours after and 200 km to the east of theturbulence encounter. The two-dimensional model windis derived from the velocity component in the direction ofmaximum wind in the sounding. Convection is initializedusing a localized surface heating. This method producesa mature convective system within about 2 hours of modelinitialization.

Using two-way interactive grid nesting, a higher res-olution domain is included in the region surrounding thecloud top. This domain has 16.67 meter grid spacing inboth the horizontal and vertical directions. This domainfocuses on the development of the convective updraftsas they overshoot the relatively undisturbed tropopauseregion. Three representative times during the develop-ment of one particular updraft are shown in Fig. 1. Figure1(a) shows that as this particular updraft overshoots thetropopause, at about 11 km AGL, the flow is initially lam-inar above the cloud. Within 5 minutes of this overshoot(Fig. 1b), wave-like perturbations in the potential tem-perature are evident above the cloud, and one phase ofthese waves has become unstable and broken over thecloud top. This breaking produces turbulent overturningof the clear-air on a horizontal scale less than 1 km. Laterin the evolution of the updraft (Fig. 1c), the turbulence re-gion has extended vertically to over 1 km above the cloudtop. Also, small turbulent eddies form along the cloud in-terface. These eddies are formed by a shearing instabil-ity, due to the strong deformation of the flow at the cloudinterface (see Grabowski and Clark 1991 for further de-tails of this instability).

In addition to the turbulent motion in the first kilome-ter above the cloud top, turbulence is also generated athigher altitudes. Figure 2 shows the existence of grav-ity wave breaking later in the cloud’s evolution. At 100minutes into the model calculation, vertically propagat-ing gravity waves generated by the convection becomeunstable and break in a narrow region above the cloud.These waves are forced by the overshooting updrafts,and the subsequent dry response. The breaking con-tinues in time, and eventually extends vertically to about14.5 km altitude, spanning approximately 30 kilometers inthe horizontal (Fig. 2c). Associated with this wave break-

FIG. 1: Three representative times during the two-dimensional model calculation illustrating the overshootof a single convective updraft. Contours of potential tem-perature (1 K intervals), and the (0.05 ��������� ) total cloudloading outline (thick). Shading denotes regions of con-vective instability outside cloud. is height AGL, and thebackground wind is from the left.

ing is turbulent mixing down to the smallest resolvablescale in the model. This breaking is due to the interactionof these vertically propagating waves with a critical level,where the flow speed equals the propagation speed ofthe waves.

3. Three-dimensional simulations

This section examines the results from a more realisticmodel calculation in three spatial dimensions. In order toexamine the development and initiation of convection in amore realistic environment, the cloud model is coupled toa large scale forecast model, MM5. An MM5 calculationbegins 24 hours prior to the turbulence encounter, andis used as initial and boundary conditions for the cloudmodel. MM5 makes a reasonable representation of theconditions surrounding the event. It produces convectionin approximately the correct area, but about an hour early

FIG. 2: Three representative times during the two-dimensional model calculation illustrating the breaking ofwaves above the convection. Contours are the same asFig. 1, except the potential temperature has 2 K intervals.

and about 100 km to the west. Nonetheless, the convec-tion develops in a similar configuration to that observed,with a cell developing in the center of two larger moremature cells. It is this center cell that was encounteredby the aircraft, and is the focus of the three-dimensionalmodeling. Within the cloud model domain, six levels ofgrid nesting are used, with the finest scale grid having 55meter horizontal and 33 meter vertical grid spacing.

Three representative times during the center cloud’sevolution are shown in Figure 3. As the updraft over-shoots the tropopause region, the isentropes are stronglycompressed forming very high stratification at the cloudboundary (Fig. 3a). Later in the evolution (Fig. 3b),the updraft has completely overshot the tropopause anda net downward buoyancy force is exerted on the top ofthe cloud. These isentropes at the cloud top are forceddownwards (Fig. 3c). During this downward response,however, a turbulent mixed layer forms at the cloud top.The result is a turbulent layer about 1 km deep, and about2 km wide.

This three-dimensional turbulence generation is sim-

FIG. 3: Three representative times during the three-dimensional model calculation illustrating the overshootof a single cloud. Contours are the same as Fig. 1. Thehorizontal axis is aligned with the mean shear vector atthe tropopause.

ilar to that seen in the two-dimensional case. In particu-lar, during the updraft reversal, which is a response to theovershoot, regions of turbulence are generated above thepenetrating updraft. The mechanism causing this turbu-lence generation may be a combination of a gravity waveresponse (as suggested by Fig. 1), or a more compli-cated response to vorticity generation by the strong buoy-ancy gradients at the boundary of the overshooting up-draft. Understanding this mechanism is a topic for futureresearch.

The three-dimensional case, however, does notshow the coherent wave breaking above the cloud as wasseen in the two-dimensional case (Fig. 2). The reasonfor this is probably a combination of three-dimensional ef-fects and the reduced wind shear; the MM5 failed to re-produce the strength of the wind shear observed in theBismarck sounding. Subsequently, the three-dimensionalcalculation possessed about one half of the wind shearof the two-dimensional calculation. This reduced windshear removed the critical level that caused the gravity

wave breaking in Fig. 2.

4. Conclusions

This study has examined the generation of turbulence inthe clear-air above deep convection. Using a numberof high resolution cloud-resolving model calculations, itwas shown that local instabilities generated turbulence ina layer 1 to 2 km deep above the cloud top. Also, in acase where the wind shear was sufficiently strong, grav-ity waves became unstable and broke up to 4 km abovecloud top, generating a turbulent layer about 30 km long.In all cases, however, the turbulence appears highly lo-calized, being surrounded by relatively laminar flow.

This study was motivated by a specific turbulenceencounter, where a commercial aircraft encounteredturbulence very close to the top of a developing cloud.These results provide some insight into some possiblemechanisms which may have led to this turbulenceencounter. Also, case studies such as this can beused to evaluate and improve strategies for turbulenceavoidance by aircraft. Further case studies are plannedfor the future.

Acknowledgments

This research was funded in part by the FAA’s Avi-ation Weather Research Program and NASA’s AviationSafety Program. This research is in response to require-ments and funding by the Federal Aviation Administration(FAA). The views expressed are those of the authors anddo not necessarily represent the official policy or positionof the FAA.

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